The Uncovered Set and the Limits of Legislative Action

2004 ◽  
Vol 12 (3) ◽  
pp. 256-276 ◽  
Author(s):  
William T. Bianco ◽  
Ivan Jeliazkov ◽  
Itai Sened
Keyword(s):  
Social Choice ◽  
Real World ◽  
Solution Concept ◽  
Collective Choice ◽  
Simulation Technique ◽  
Legislative Action ◽  
Uncovered Set ◽  
Spatial Voting ◽  
Voting Games

We present a simulation technique for sorting out the size, shape, and location of the uncovered set to estimate the set of enactable outcomes in “real-world” social choice situations, such as the contemporary Congress. The uncovered set is a well-known but underexploited solution concept in the literature on spatial voting games and collective choice mechanisms. We explain this solution concept in nontechnical terms, submit some theoretical observations to improve our theoretical grasp of it, and provide a simulation technique that makes it possible to estimate this set and thus enable a series of tests of its empirical relevance.

scholarly journals In Search of the Uncovered Set

2007 ◽  
Vol 15 (1) ◽  
pp. 21-45 ◽  
Author(s):  
Nicholas R. Miller
Keyword(s):  
Computational Algorithm ◽  
Voting Theory ◽  
Legislative Action ◽  
Uncovered Set ◽  
Political Analysis ◽  
Spatial Voting ◽  
Voting Games ◽  
General Relevance ◽  
Straight Line ◽  
Theoretical Considerations

This paper pursues a number of theoretical explorations and conjectures pertaining to the uncovered set in spatial voting games. It was stimulated by the article “The Uncovered Set and the Limits of Legislative Action” by W. T. Bianco, I. Jeliazkov, and I. Sened (2004, Political Analysis 12:256—78) that employed a grid-search computational algorithm for estimating the size, shape, and location of the uncovered set, and it has been greatly facilitated by access to the CyberSenate spatial voting software being developed by Joseph Godfrey. I bring to light theoretical considerations that account for important features of the Bianco, Jeliazkov, and Sened results (e.g., the straight-line boundaries of uncovered sets displayed in some of their figures, the “unexpectedly large” uncovered sets displayed in other figures, and the apparent sensitivity of the location of uncovered sets to small shifts in the relative sizes of party caucuses) and present theoretical insights of more general relevance to spatial voting theory.

scholarly journals Computing the Yolk in Spatial Voting Games without Computing Median Lines

2019 ◽  
Vol 33 ◽  
pp. 2012-2019
Author(s):  
Joachim Gudmundsson ◽  
Sampson Wong
Keyword(s):  
Upper Bound ◽  
Linear Time ◽  
Search Technique ◽  
Important Concept ◽  
Uncovered Set ◽  
Spatial Voting ◽  
Voting Games ◽  
Parametric Search ◽  
Linear Time Algorithms

The yolk is an important concept in spatial voting games: the yolk center generalises the equilibrium and the yolk radius bounds the uncovered set. We present near-linear time algorithms for computing the yolk in the plane. To the best of our knowledge our algorithm is the first that does not precompute median lines, and hence is able to break the best known upper bound of O(n4/3) on the number of limiting median lines. We avoid this requirement by carefully applying Megiddo’s parametric search technique, which is a powerful framework that could lead to faster algorithms for other spatial voting problems.

Applications of Shapley-Owen Values and the Spatial Copeland Winner

2011 ◽  
Vol 19 (3) ◽  
pp. 306-324 ◽  
Author(s):  
Joseph Godfrey ◽  
Bernard Grofman ◽  
Scott L. Feld
Keyword(s):  
House Of Representatives ◽  
A Priori ◽  
Solution Concept ◽  
Strong Point ◽  
Political Analysis ◽  
Spatial Voting ◽  
Voting Games ◽  
Ideological Space ◽  
The U.S ◽  
Copeland Winner

The Shapley-Owen value (SOV, Owen and Shapley 1989, Optimal location of candidates in ideological space. International Journal of Game Theory 125–42), a generalization of the Shapley-Shubik value applicable to spatial voting games, is an important concept in that it takes us away from a priori concepts of power to notions of power that are directly tied to the ideological proximity of actors. SOVs can also be used to locate the spatial analogue to the Copeland winner, the strong point, the point with smallest win-set, which is a plausible solution concept for games without cores. However, for spatial voting games with many voters, until recently, it was too computationally difficult to calculate SOVs, and thus, it was impossible to find the strong point analytically. After reviewing the properties of the SOV, such as the result proven by Shapley and Owen that size of win sets increases with the square of distance as we move away from the strong point along any ray, we offer a computer algorithm for computing SOVs that can readily find such values even for legislatures the size of the U.S. House of Representatives or the Russian Duma. We use these values to identify the strong point and show its location with respect to the uncovered set, for several of the U.S. congresses analyzed in Bianco, Jeliazkov, and Sened (2004, The limits of legislative actions: Determining the set of enactable outcomes given legislators preferences. Political Analysis 12:256–76) and for several sessions of the Russian Duma. We then look at many of the experimental committee voting games previously analyzed by Bianco et al. (2006, A theory waiting to be discovered and used: A reanalysis of canonical experiments on majority-rule decision making. Journal of Politics 68:838–51) and show how outcomes in these games tend to be points with small win sets located near to the strong point. We also consider how SOVs can be applied to a lobbying game in a committee of the U.S. Senate.

Testing the Predictions of the Multidimensional Spatial Voting Model with Roll Call Data

2007 ◽  
Vol 16 (2) ◽  
pp. 179-196 ◽  
Author(s):  
Gyung-Ho Jeong
Keyword(s):  
Predictive Power ◽  
Empirical Test ◽  
Ideal Point ◽  
Solution Concept ◽  
Point Estimation ◽  
Roll Call ◽  
Uncovered Set ◽  
Spatial Voting ◽  
Spatial Voting Model ◽  
Voting Model

This paper develops a procedure for locating proposals and legislators in a multidimensional policy space by applying agenda-constrained ideal point estimation. Placing proposals and legislators on the same scale allows an empirical test of the predictions of the spatial voting model. I illustrate this procedure by testing the predictive power of the uncovered set—a solution concept of the multidimensional spatial voting model—using roll call data from the U.S. Senate. Since empirical tests of the predictive power of the uncovered set have been limited to experimental data, this is the first empirical test of the concept's predictive power using real-world data.

Stability and Centrality of Legislative Choice in the Spatial Context

1987 ◽  
Vol 81 (2) ◽  
pp. 539-553 ◽  
Author(s):  
Bernard Grofman ◽  
Guillermo Owen ◽  
Nicholas Noviello ◽  
Amihai Glazer
Keyword(s):  
Infinite Number ◽  
Majority Rule ◽  
Solution Concept ◽  
Spatial Context ◽  
Core Outcome ◽  
Legislative Voting ◽  
Spatial Voting ◽  
Voting Games ◽  
Legislative Choice ◽  
Copeland Winner

Majority-rule spatial voting games lacking a core still always present a “near-core” outcome, more commonly known as the Copeland winner. This is the alternative that defeats or ties the greatest number of alternatives in the space. Previous research has not tested the Copeland winner as a solution concept for spatial voting games without a core, lacking a way to calculate where the Copeland winner was with an infinite number of alternatives. We provide a straightforward algorithm to find the Copeland winner and show that it corresponds well to experimental outcomes in an important set of experimental legislative voting games. We also provide an intuitive motivation for why legislative outcomes in the spatial context may be expected to lie close to the Copeland winner. Finally, we show a connection between the Copeland winner and the Shapley value and provide a simple but powerful algorithm to calculate the Copeland scores of all points in the space in terms of the (modified) power values of each of the voters and their locations in the space.

The uncovered set in spatial voting games

1987 ◽  
Vol 23 (2) ◽  
pp. 129-155 ◽  
Author(s):  
Scott L. Feld ◽  
Bernard Grofman ◽  
Richard Hartly ◽  
Marc Kilgour ◽  
Nicholas Miller ◽  
...  
Keyword(s):  
Uncovered Set ◽  
Spatial Voting ◽  
Voting Games

Social Choice in the Real World

1993 ◽  
Vol 16 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Eerik Lagerspetz
Keyword(s):  
Social Choice ◽  
Real World ◽  
The Real

Collective Choice and Mutual Knowledge Structures

1998 ◽  
Vol 01 (02n03) ◽  
pp. 221-236 ◽  
Author(s):  
Diana Richards ◽  
Brendan D. McKay ◽  
Whitman A. Richards
Keyword(s):  
Complex System ◽  
Social Choice ◽  
Group Decision ◽  
Knowledge Structure ◽  
Collective Choice ◽  
Sense Data ◽  
Mutual Knowledge ◽  
Interacting Agents ◽  
Aggregation Of Information ◽  
Domain Independent

The conditions under which the aggregation of information from interacting agents results in a stable or an unstable collective outcome is an important puzzle in the study of complex systems. We show that if a complex system of aggregated choice respects a mutual knowledge structure, then the prospects of a stable collective outcome are considerably improved. Our domain-independent results apply to collective choice ranging from perception, where an interpretation of sense data is made by a collection of perceptual modules, to social choice, where a group decision is made from a set of preferences held by individuals.

On β-Plurality Points in Spatial Voting Games

2021 ◽  
Vol 17 (3) ◽  
pp. 1-21
Author(s):  
Boris Aronov ◽  
Mark De Berg ◽  
Joachim Gudmundsson ◽  
Michael Horton
Keyword(s):  
Spatial Voting ◽  
Voting Games ◽  
Equal Distance ◽  
Alternative Proposal

Let V be a set of n points in mathcal R d , called voters . A point p ∈ mathcal R d is a plurality point for V when the following holds: For every q ∈ mathcal R d , the number of voters closer to p than to q is at least the number of voters closer to q than to p . Thus, in a vote where each  v ∈ V votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal  p will not lose against any alternative proposal  q . For most voter sets, a plurality point does not exist. We therefore introduce the concept of β-plurality points , which are defined similarly to regular plurality points, except that the distance of each voter to p (but not to  q ) is scaled by a factor  β , for some constant 0< β ⩽ 1. We investigate the existence and computation of β -plurality points and obtain the following results. • Define β * d := {β : any finite multiset V in mathcal R d admits a β-plurality point. We prove that β * d = √3/2, and that 1/√ d ⩽ β * d ⩽ √ 3/2 for all d ⩾ 3. • Define β ( p, V ) := sup {β : p is a β -plurality point for V }. Given a voter set V in mathcal R 2 , we provide an algorithm that runs in O ( n log n ) time and computes a point p such that β ( p , V ) ⩾ β * b . Moreover, for d ⩾ 2, we can compute a point  p with β ( p , V ) ⩾ 1/√ d in O ( n ) time. • Define β ( V ) := sup { β : V admits a β -plurality point}. We present an algorithm that, given a voter set V in mathcal R d , computes an ((1-ɛ)ċ β ( V ))-plurality point in time O n 2 ɛ 3d-2 ċ log n ɛ d-1 ċ log 2 1ɛ).

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